"She's done very well to get where she has, but I think there is a danger that we've gone beyond the strong image with the marshalling of the troops, to her becoming nearly a parody of herself with the tank-riding and bull-riding and flag-waving", a senior SNP lawmaker said.
Davidson led her party to its best result in Scotland for three decades, in contrast to Conservative Prime Minister Theresa May's dismal showing elsewhere in the UK.
The Tories have fought a campaign relentlessly focused on opposing a second independence referendum.
The calls came in the wake of 2015's Brexit referendum, which Scottish voters overwhelmingly rejected, but will be forced to accept as long as they remain part of the UK.
Commenting on the results, Ms Davidson said the Scottish nationalists should now agree to take a second referendum "off the table".
Kezia Dugdale, Labour's leader in Scotland, wrote that it made them no better than the Tories, and frankly it's hard to see how she's wrong.
Sturgeon admitted her party, which lost 21 seats across Scotland, "suffered some bitter losses".
In East Dunbartonshire, Liberal Democrat Jo Swinson regained the seat from the SNP's John Nicolson.
Ms Davidson, tipped by many as a future UK Tory leader, hailed a "historic" night for her party and said the result ended the prospect of another independence vote soon.
He said: "Instead of people shouting from the opposition benches around these issues, you've got a bunch of people elected as Scottish Conservatives, right in the party of government, who can take those arguments and ensure when a Brexit deal is negotiated, it is the interests of Scottish fishing that are right at the forefront". Her stance, a far cry from that of Sturgeon, was based on understanding "the street." .
The leader of the Labour Party, Jeremy Corbyn, is adamant that May ought to pay the price of her miscalculation. We have to wait and see how things shake out.
"78 per cent of Glasgow North voted to remain in the European Union a year ago, I think it shows they want Scotland's voice to be heard".
First Minister Nicola Sturgeon has conceded her plans for a second vote were "undoubtedly" a factor in the result and has said she will reflect on the results. This Brexit election was supposed to equip the government with the authority to agree and implement its plans to take the United Kingdom out of the EU. "We got more seats. than all the other parties combined".
The Tory, who is also a football referee, won 22,637 votes, easily beating Mr Robertson who polled 18,478. The Tories also benefited because they have in Mrs Davidson a leader who, unlike Mrs May, comes across as a human being.
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But EU officials are sceptical that May's position has changed, just as they are doubtful about the feasibility of either option. However, it seems unlikely he will be able to resist public comment on the Brexit process, which he has described as a "tragedy".
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He closed with a 5-under 67, only realizing after his par on the final hole that a birdie would have set yet another U.S. Koepka said the world number one had called him on Saturday, offering some advice which came in handy.
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I didn't feel like today I was playing slower than I was in the other matches. 'I think he's probably a bit less confident. The 30-year-old has won eight of their 10 previous meetings, most recently at the ATP World Tour Finals last November.